Country Workshop manufactures both finished and unfinished furniture for the home. The estimated quantities demanded each week of its rolltop desks in the finished and unfinished versions are x and y units when the corresponding unit prices, in dollars, are described, respectively, in the following equations.
p = 310-1x-1/2y
q = 730-1/2x-1/7y
(a) What is the weekly total revenue function R(x,y)?
R(x,y) = xp + yq
x(310-1x-1/2y) + y(730 -1/2x -1/7y)
310x -x^2 -1/2xy + 730y -1/2xy -1/7y^2
= -x^2 -1/7y^2 -xy + 310x + 730y
fda
To find the weekly total revenue function R(x,y), we need to multiply the quantity demanded (q) by the corresponding unit price (p).
Given that the unit price for the finished version of rolltop desks is given by p = 310 - x - (1/2)y, and the quantity demanded is given by q = 730 - (1/2)x - (1/7)y, we can substitute these equations into the formula for total revenue.
R(x,y) = p * q
We substitute p and q into the equation:
R(x,y) = (310 - x - (1/2)y) * (730 - (1/2)x - (1/7)y)
Now we can simplify and solve for R(x,y).